On stabilizing properties of solutions of the Riccati difference equation

Monotonicity and stabilizing properties of solutions of the Riccati difference equation (RDE) are discussed. The author considers the problem of selecting an initial condition for the RDE in such a way that the update of the Kalman filter gain can be stopped at any time and the resulting frozen filter is asymptotically stable. The author also considers the case in which the initial condition of the RDE may be less than the asymptotic solution. The results are relevant to control and observer design, including the stability of finite-time horizon discrete-time predictive control.<
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